Suppose we build a logistic regression model to classify patients into HEALTHY or NOT-HEALTHY based on their age in years above sixty

 Please show all your work. Correct answers with no work shown will receive a grade of zero.

 Allowed aids: course textbook; course notes and other course material posted on Learn; external material linked to in the lecture slides.

 Please submit your solutions, in pdf format, to Learn, under Submit -> Dropbox -> Test 2.

 Question 1: Linear models [4 points] 

Suppose we have the following (x,y) datapoints: (0,-1), (1,0), (1,2), (2,3), (3,4), (4,8). Suppose we are given a linear model of the form y=mx+b that uses x to predict y. Suppose that running the model on the above data points gives the residual plot shown below (with x on the horizontal axis and residuals on the vertical axis).

Without making any other assumptions, what is the linear model?

Question 2: Logistic regression [3 points]

Suppose we build a logistic regression model to classify patients into HEALTHY or NOT-HEALTHY based on their age in years above sixty (call it p; for example, for a 62-year-old person, years above sixty = 2), fitness (call it q; zero if the patient exercises regularly, one otherwise), and cholesterol level (call it r). Suppose the model is

Will this model make the same or different prediction for the following patients? 

Patient 1: 60-year-old person who exercises regularly, with cholesterol level 3.0

Patient 2: 60-year-old person who does not exercise regularly, with cholesterol level 3.5

Question 3: Naïve Bayes Classifier [4 points] 

Suppose we have the following data set in which A and B are features and C is the class label. 

For a new datapoint with A = Yes and B = 45, would Naïve Bayes predict C = Yes or C = No?

Question 4: Decision Trees [4 points] 

Consider the following dataset in which F, G and H are features and C is the class label. Explain which root node would be chosen by the entropy-based decision tree classifier described in the lecture slides. 

Question 5: Cross-validation [4 points] 

Suppose you are the manager of a data analytics company. One of your junior analysts has applied a decision tree classification algorithm to a labeled data set D and calculated two things: 

1)  the accuracy of the decision tree on D using 10-fold cross validation, and

2)  the accuracy of the decision tree on D using an 80%-train / 20%-test split of the data 

She says to you: “With 10-fold cross validation, we get a 12% improvement in accuracy compared to the 80/20 split. I think that for classifying new data, we should use 10-fold cross validation”. You realize that the analyst found something interesting, but she is also lacking a fundamental understanding of data mining. What is incorrect in the analyst’s statement that “I think that for classifying new data, we should use 10-fold cross validation”?

Question 6: Leave-one-out cross-validation [4 points]